Remark We could have arrived at thm:DecomposableQCQPSDPguarantee by using the results in [1]} who describe a chordality-detection procedure for SDPs with chordal sparsity pattern. However, this procedure seemed more complicated than proving chordality of arrow-head matrices directly here. It is nonetheless important to note that the above result is not the first of its kind, but can be obtained directly from known results in literature. Still, to the best of our knowledge, the context in which we use this technique is original.

